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54The axiomatization of randomnessJournal of Symbolic Logic 55 (3): 1143-1167. 1990.We present a faithful axiomatization of von Mises' notion of a random sequence, using an abstract independence relation. A byproduct is a quantifier elimination theorem for Friedman's "almost all" quantifier in terms of this independence relation
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106Algorithmic information theoryJournal of Symbolic Logic 54 (4): 1389-1400. 1989.We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on Godel's first incompleteness theorem
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10Language Evolution: Enlarging the PictureIn David McFarland, Keith Stenning & Maggie McGonigle (eds.), The Complex Mind, Palgrave-macmillan. pp. 264-282. 2012.
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26The representation of Takeuti's $$\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $$ -operatorStudia Logica 42 (4): 407-415. 1983.Gaisi Takeuti has recently proposed a new operation on orthomodular latticesL, $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ :P(L)»L. The properties of $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ suggest that the value of $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ (A) (A) $ \subseteq $ L) corresponds to the degree in which the elements ofA behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular …Read more
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3054A formalization of kant’s transcendental logicReview of Symbolic Logic 4 (2): 254-289. 2011.Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem o…Read more
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156Semantics as a foundation for psychology: A case study of Wason's selection task (review)Journal of Logic, Language and Information 10 (3): 273-317. 2001.We review the various explanations that have been offered toaccount for subjects'' behaviour in Wason ''s famous selection task. Weargue that one element that is lacking is a good understanding ofsubjects'' semantics for the key expressions involved, and anunderstanding of how this semantics is affected by the demands the taskputs upon the subject''s cognitive system. We make novel proposals inthese terms for explaining the major content effects of deonticmaterials. Throughout we illustrate with…Read more
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47A little logic goes a long way: basing experiment on semantic theory in the cognitive science of conditional reasoningCognitive Science 28 (4): 481-529. 2004.
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39Reasoning in Non-probabilistic Uncertainty: Logic Programming and Neural-Symbolic Computing as ExamplesMinds and Machines 27 (1): 37-77. 2017.This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty ; and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: logic programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of input/output logic for …Read more
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52A logic of visionLinguistics and Philosophy 23 (1): 1-92. 2000.This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and Johnson-Laird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessarily differs from situation semantics. On the psychological side, our main inspiration is Marr's (1982) theory of vision, which can easily accomodate fallible perception. In Marr's theory, vision is a m…Read more
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102Logic in the study of psychiatric disorders: Executive function and rule-followingTopoi 26 (1): 97-114. 2007.Executive function has become an important concept in explanations of psychiatric disorders, but we currently lack comprehensive models of normal executive function and of its malfunctions. Here we illustrate how defeasible logical analysis can aid progress in this area. We illustrate using autism and attention deficit hyperactivity disorder (ADHD) as example disorders, and show how logical analysis reveals commonalities between linguistic and non-linguistic behaviours within each disorder, and …Read more
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8Event Calculus, Nominalisation, and the ProgressiveLinguistics and Philosophy 26 (4): 381-458. 2003.
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67Logic as Marr's Computational Level: Four Case StudiesTopics in Cognitive Science 7 (2): 287-298. 2015.We sketch four applications of Marr's levels-of-analysis methodology to the relations between logic and experimental data in the cognitive neuroscience of language and reasoning. The first part of the paper illustrates the explanatory power of computational level theories based on logic. We show that a Bayesian treatment of the suppression task in reasoning with conditionals is ruled out by EEG data, supporting instead an analysis based on defeasible logic. Further, we describe how results from …Read more
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43Sieg has proposed axioms for computability whose models can be reduced to Turing machines. This lecture will investigate to what extent these axioms hold for reasoning. In particular we focus on the requirement that the configurations that a computing agent (whether human or machine) operates on must be ’immediately recognisable’. If one thinks of reasoning as derivation in a calculus, this requirement is satisfied; but even in contexts which are only slightly less formal, the requirement cannot…Read more
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36Semantic Interpretation as Computation in Nonmonotonic Logic: The Real Meaning of the Suppression TaskCognitive Science 29 (6): 919-960. 2005.Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of pa…Read more
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32A little logic goes a long way: basing experiment on semantic theory in the cognitive science of conditional reasoningCognitive Science 28 (4): 481-529. 2004.
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41The representation of Takeuti's *20c ||_ -operatorStudia Logica 42 (4). 1983.Gaisi Takeuti has recently proposed a new operation on orthomodular lattices L, ⫫: $\scr{P}(L)\rightarrow L$ . The properties of ⫫ suggest that the value of ⫫ $(A)(A\subseteq L)$ corresponds to the degree in which the elements of A behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular lattices L and the existence of two-valued homomorphisms on L
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755In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesi…Read more
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53Discourse processing in attention-deficit hyperactivity disorder (adhd)Journal of Logic, Language and Information 17 (4): 467-487. 2008.ADHD is a psychiatric disorder characterised by persistent and developmentally inappropriate levels of inattention, impulsivity and hyperactivity. It is known that children with ADHD tend to produce incoherent discourses, e.g. by narrating events out of sequence. Here the aetiology of ADHD becomes of interest. One prominent theory is that ADHD is an executive function disorder, showing deficiencies of planning. Given the close link between planning, verb tense and discourse coherence postulated …Read more
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37Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and ChaterThinking and Reasoning 22 (3): 355-368. 2016.This reply to Oaksford and Chater’s ’s critical discussion of our use of logic programming to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ra…Read more
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16Explaining intersubjectivity. A comment on Arie Verhagen, Constructions of IntersubjectivityCognitive Linguistics 19 (1). 2008.
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80Language, linguistics and cognitionIn Ruth M. Kempson, Tim Fernando & Nicholas Asher (eds.), Philosophy of Linguistics, North Holland. 2012.
Amsterdam, North Holland, Netherlands
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History of Western Philosophy |